CAIE P1 2012 June — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionJune
TopicStraight Lines & Coordinate Geometry

9 The coordinates of \(A\) are \(( - 3,2 )\) and the coordinates of \(C\) are (5,6). The mid-point of \(A C\) is \(M\) and the perpendicular bisector of \(A C\) cuts the \(x\)-axis at \(B\).
  1. Find the equation of \(M B\) and the coordinates of \(B\).
  2. Show that \(A B\) is perpendicular to \(B C\).
  3. Given that \(A B C D\) is a square, find the coordinates of \(D\) and the length of \(A D\).